A365184 G.f. satisfies A(x) = 1 + x*A(x)^5*(1 + x).

1, 1, 6, 45, 395, 3775, 38146, 400826, 4335455, 47951065, 539823620, 6165377836, 71261299056, 831990025420, 9797505040130, 116235417614900, 1387958781395535, 16668362761081560, 201190667288072005, 2439418470063468505, 29698136499328762445

Offset: 0

Author

Seiichi Manyama, Aug 25 2023

Keywords

• nonn

Links

• Seiichi Manyama, Table of n, a(n) for n = 0..898

Crossrefs

Cf. A002295, A365185, A365186, A365187, A365188, A365189.

Cf. A364475, A365178.

Cf. A002294, A349332.

Programs

PARI

a(n) = sum(k=0, n, binomial(k, n-k)*binomial(5*k, k)/(4*k+1));

Formula

a(n) = Sum_{k=0..n} binomial(5*k+1,k) * binomial(k,n-k)/(5*k+1) = Sum_{k=0..n} binomial(k,n-k) * A002294(k).